Audio reproduction systems are used in a variety of applications including radio receivers, stereo equipment, speakerphone systems, and a number of other environments. Audio reproduction systems take signals representing audio information and convert them to sound waves. The most common means of converting electrical energy to acoustical energy in sound systems is what is known as an electrodynamic driver, which operates according to the forces generated when an electric current interacts with a magnetic field.
Distortion is a measure of the error in the output of an audio reproduction system which characterized by the extent to which the acoustical signal does not follow a linear transformation of the electrical input to the degree of accuracy desired.
Two of the major sources of distortion in the process of converting audio information into sound are related to two processes with similar names: one is called a transconductance and the other is called a transduction. The first process, transconductance, stated simply, is a natural process which takes a voltage input to a loudspeaker, an apparatus containing a voice coil, magnet, and diaphragm herein referred to as a driver, and converts this voltage into electrical current flowing in the voice coil. The second process, transduction, converts said current in the voice coil into the motion of the voice coil thereby moving an air mass coupled by some means such as a diaphragm connected to the voice coil.
Transconductance can be described more formally as a necessary conditioning of an audio signal to produce a transducer drive signal. The signal conditioning process may be accomplished in a digital or analog form, the common method is to convert the audio signal to a voltage level, and then use this voltage to drive the impedance of the voice coil, providing current through the coil. This current then results in coil/diaphragm motion (electromechanical transduction). The signal conditioning may utilize a linear amplifier, in which one voltage signal is converted to another with greater driving power.
Unfortunately, distorting factors due to nonlinear effects influence both of these processes, which will be explained with reference to the following figure. FIG. 1 is an illustration of a typically used electrodynamic transducer, a conventional voice coil transducer 300. The frame 301 holds the cone, or diaphragm 302. The diaphragm 302 is acted upon by voice coil 303 which acts as a motor, causing the diaphragm 302 to vibrate and create pressure waves in the ambient air. Voice coil 303 includes a coil of wire wound around a tube or former. Voice coil 303 receives an electrical current, which is acted upon by the static magnetic field developed by the permanent magnet 304 and iron assembly 305 in the annular gap 306 in which voice coil 303 rides. The additional magnetic field from voice coil 303, which is induced by the external current driven through voice coil 303, interacts with the static magnetic field due to the permanent magnet 304 and iron assembly 305 within the annular gap 306, causing the voice coil 303 to move forward (toward the listener, to the right in FIG. 3) or backward (away from listener, to the left in FIG. 3). Two concentric springs, the spider 307 and surround 308, provide suspension for the voice coil/diaphragm assembly, holding it in place in a concentric position and pulling it back to an equilibrium position when there is no signal applied to voice coil 303. A dome 309 acts as a dust cap and as a diffuser for high frequency sound. The example illustrates the general process of electromechanical transduction from which many specific implementations may be derived.
There are a number of causes of audio distortion that involve the structure and operation of the voice coil transducer 300. These are due to nonlinear effects that are an intrinsic part of voice coil transducers. These nonlinear effects are largely caused by the nonlinearities in the coil motor factor, in the restoring force factor of the coil/diaphragm assembly suspension, and in the impedance of the coil. Other nonlinear effects also contribute to the distortion.
Nonlinearities in the motor factor in a voice coil transducer result from the fact that the coil and the region of uniform static magnetic field are limited in size, coupled with the fact that the coil moves relative to the static field. The actual size of the static magnetic field region, and its size relative to the voice coil, represents engineering and economic compromises. For a voice coil in a transducer, a stronger field results in a larger motor factor, and hence a larger motive force per given coil current magnitude. As the field falls off away from the annular gap 306, the motive force is reduced. The motive force per unit coil current is defined as the motor factor, and depends on the geometry of the coil and on the shape and position of the coil with respect to the static magnetic field configuration, the latter being generated by the permanent magnet or magnets and guided by the magnetic pole structures. This motor factor is usually denoted as the Bl factor, and is a function of x, the outward displacement of the coil/diaphragm assembly away from its equilibrium position (which the transducer relaxes to after the driving audio signal ceases). As used herein, x is positive when the coil/diaphragm assembly is displaced from equilibrium in the direction of the listener, i.e., towards the front of the driver.
FIG. 2 represents data for actual parameters of a transducer from a small loudspeaker system. The large signal (LS) operating parameters shown in FIG. 2 were obtained using a commonly available laser metrology system. The magnitude of Bl is shown by curve 401 as a function of the displacement x of the coil/diaphragm assembly from the no-signal equilibrium position, which is indicated in FIG. 2 by a zero on the horizontal axis; at that position, no elastic restoring force is applied to the coil/diaphragm assembly. The unit for Bl is Newton/Ampere (or N/A). The highly non-constant nature of the Bl factors of commercial voice coil transducers as a function of signal level is recognized in the current art. As the audio signal increases in magnitude, the coil tends to move away from the region of maximal static magnetic field, and the motor factor decreases—thus effecting a less uniform coil movement and distorting the sound wave.
Referring again to FIG. 1, as pointed out above, the cone suspension is typically axially symmetric and typically includes two parts: a corrugated suspension near the coil, typically referred to as the spider 307, and the surround 308 connecting the large end of cone 302 to the frame 301 of the driver. These two suspensions together act as an effective spring, which provides a restoring force to the coil/diaphragm assembly and determines the equilibrium position of the assembly to which it relaxes when not being driven. This effective spring restoring force is again a highly non-linear function of coil/cone axial position x; that is to say, the effective spring stiffness varies significantly as a function of x. In FIG. 2, curve 402 shows a graph of K, the spring stiffness, as a function of x for the driver transducer mentioned above. Spring stiffness K is expressed in units of N/mm (i.e., Newtons per millimeter).
The mechanical equation of motion for the transducer can be approximated as a second order ordinary differential equation (ODE) in the position x of the coil/diaphragm assembly, treated as if it were a rigid piston. This is the electromechanical (or current-to-displacement) transduction equation:
                                          m            ⁢                                                  ⁢                                                            ⅆ                  2                                ⁢                x                                            ⅆ                                  t                  2                                                              +                                    R                              m                ⁢                                                                  ⁢                s                                      ⁢                                          ⅆ                x                                            ⅆ                t                                              +                      x            ⁢                                                  ⁢                          K              ⁡                              (                x                )                                                    =                              Bl            ⁡                          (              x              )                                ⁢                                          ⁢                      i            ⁡                          (              t              )                                                          (        1        )            where m is the mass of the assembly plus a factor for the mass of air being moved; d2x/dt2 is used as the term for acceleration and dx/dt is used as the term for velocity; Rms represents the effective drag coefficient experienced by the assembly, mainly due to air resistance and suspension friction; K(x) is the position dependent effective spring stiffness due to the elastic suspension; Bl(x) is the position dependent motor factor; and i(t) is the time dependent voice-coil current, which relates via transconductance to the input audio signal and constitutes the control variable.
Further nonlinearities arise due to other electrodynamical effects caused by the application of the audio signal to the transducer voice-coil. Typically, current is supplied to the coil by converting the audio information into a voltage, V(t), which is imposed across the terminals of the voice coil. However, the resulting coil current varies both out of phase and nonlinearly with this voltage. The phase lag arises both because the voice coil's effective impedance has a reactive component, and because the electromechanical transduction of the coil current into coil motion through the static magnetic field induces a back-Electromotive Force (BEMF) voltage term in the coil circuit.
The imposed voltage gives rise to the drive (coil) current, which is determined via the transconductance (voltage-to-current) process, conventionally expressed by the following approximate circuit equation:
                              V          ⁡                      (            t            )                          =                                            i              ⁡                              (                t                )                                      ⁢                                                  ⁢                          R              e                                +                                                    L                e                            ⁡                              (                x                )                                      ⁢                                                  ⁢                                          ⅆ                i                                            ⅆ                t                                              +                                    Bl              ⁡                              (                x                )                                      ⁢                                                  ⁢                                          ⅆ                x                                            ⅆ                t                                                                        (        2        )            where the BEMF is represented by the last term on the right hand side (a product of Bl(x) and coil velocity). The resistance of the coil is Re. The coil's effective inductance, Le(x), is a function x because it depends upon the instantaneous position of the coil relative to the magnetic pole structure and its air gap. In FIG. 2, curve 403 shows a typical graph of the position dependence of coil inductance Le(x) at low audio frequencies. The units of Le are mH (milli-Henries), and the values of Le shown in curve 403 have been multiplied by a factor 10 to render the graph more readable.
There are well-recognized nonlinearities in the drive current as function of voltage caused by the dependence of both the effective coil impedance and of the motor's BEMF on the relative position of the coil to the magnet assembly. The spring stiffness of the coil/diaphragm assembly likewise depends on coil position, as does the motor factor—resulting in well-recognized sources of nonlinearity. Additionally, more gradual changes of coil impedance due to Ohmic and environmental heating cause the drive-current response to drift over time, which causes the effective acoustic gain of a voltage amplifier/driver system to drift as well. All these effects cause power and frequency dependent distortions of the audio signal.
In summary, voice coil drivers driven by voltage amplifiers in the audio range are susceptible to two main sources of nonlinearities. The first is due to the fact that the inductance of the driver, Le(x), is a non-constant function of driver cone displacement, and the second is due to the nonlinear nature of the back electromotive force, Bl(x)dx/dt, which itself is due to the fact that the motor factor of the driver is a non-constant function of driver cone displacement.
From the equation V(t)=i(t)Re+Le(x)di/dt+Bl(x)dx/dt, it can be seen that if a current-source amplifier is used that drives current, rather than a voltage—source amplifier, then several of the nonlinearities and temperature related variations associated with the transconductive process, i(t)Re,Le(x)di/dt, and Bl(x)dx/dt drop out. This is primarily the reason that some advocate the use of current amplifiers to reduce distortion in moving coil loudspeaker systems. It is also important to note that the transconductance equation is not independent of the transduction equation. Thus, when an audio circuit is driven by a voltage amplifier, it is described by a nonlinear coupled third order differential equation, while when an audio circuit is driven by a current amplifier, it is described by a nonlinear second order differential equation. Therefore, using a current amplifier in an audio circuit significantly simplifies the dynamics of an audio circuit. This simplification may be important in applications that attempt to eliminate the nonlinearities of the mechanical system via signal processing techniques.
Despite the distortion reducing advantages that current amplifiers have over voltage amplifiers, the fact remains that nearly all amplifiers sold today are voltage amplifiers. There are a number of reasons for this. One primary reason may be that amplifiers and loudspeaker drivers are not typically designed and built-in an integrated and optimal fashion. The operating stability and robustness of current-source amplifiers is highly dependent on the particular properties of the driver attached to it, especially inductance, while such is not case with voltage amplifiers. For example, changing the length of a speaker-to-amplifier interconnection cable, changing the type of driver, or removing the driver, all greatly affect a current amplifier. In addition, the inductance of a given driver, which depends on frequency, tends to raise the gain of current amplifiers at high-frequencies, thus jeopardizing their correct operation.
Although the effective acoustic gain of voice coil drivers driven by voltage amplifiers drifts as a function of the resistance of the driver coil, which can vary as a function of the temperature of the coil, voltage amplifiers still have a number of key advantages. One of these advantages is that the back electromotive force supplies a certain amount of mechanical damping to the speaker system. Another is that voltage amplifiers are much more stable when driving inductive loads, so their stability is improved to a great extent regardless of the type of voice-coil driver being driven. In contrast, current amplifiers have the advantage of reducing distortion, but being less stable and robust at high frequencies.
Accordingly, an amplifier referred to as a variable impedance amplifier has been proposed that exhibits characteristics of both a current amplifier and a voltage amplifier. In order to describe the variable impedance amplifier, refer now to FIGS. 3A and 3B illustrating circuit diagrams for a standard voltage amplifier and current amplifier, respectively.
Referring to FIG. 3A, the voltage amplifier 200 includes an operational amplifier 202 that has two inputs; one for power 204 and one for an input voltage signal W, which is input through resistor R2. The output of the operational amplifier 202 is amplified voltage V. The voltage amplifier 200 includes a voltage sensing feedback path 208 for sensing the voltage V applied to the driver load 206. The voltage sensing feedback path 208 comprises resistor R1 coupled to the input voltage signal W at the output of resistor R2 and the amplified voltage V. The amplified voltage V is applied to driver load 206, which has some impedance value Z. The amplified voltage V of the voltage amplifier 200 is
  V  =            -              (                              R            1                                R            2                          )              ⁢          W      .      
Referring to FIG. 3B, the current amplifier 220 is similar to the voltage amplifier 200, but includes a current sensing feedback path 222, rather than a voltage sensing feedback path 208, for sensing the current applied to the driver 224. The current sensing feedback path 222 includes a resistor R3 coupled between the input voltage signal W at the output of resistor R2 and the resistance of the driver, Rs. The current output by the operational amplifier 228 is
  I  =            -                                    R            s                    +          Z                          R          s                      ⁢          (                        R          3                          R          2                    )        ⁢          W      .      
FIG. 4 is a circuit diagram illustrating a conventional variable impedance amplifier, which combines aspects of the voltage amplifier 200 and the current amplifier 220. The variable impedance amplifier 300 includes an operational amplifier 228, input power 304, voltage signal W, and driver load 306. The variable impedance amplifier 300 applies a mixture of both forms of feedback from the voltage amplifier 200 and the current amplifier 220 by including a voltage sensing feedback path 308 and a current sensing feedback path 322 operating in parallel.
By applying a mixture both forms of feedback, it is possible to define the output impedance of the amplifier 300, thereby defining a fixed percentage to which the variable impedance amplifier 300 performs as a current amplifier or a voltage amplifier during operation. To obtain some of the desirable audio properties of a vacuum tube amplifier for example, an output impedance of about 4 to 6 ohms would be needed, assuming an 8 ohm load (the assumed nominal load impedance). A designer could change the relative impedance for a given version of the variable impedance amplifier 300 by changing the values for R1 and R2 relative to the fixed driver load resistance.
There are several problems with this approach. One problem is that it was based on the assumption that the driver load 306 has fixed impedance, which is not the case. A driver will have various dips and peaks in its impedance curve as a function of frequency, as shown in FIG. 5.
FIG. 5 depicts a graph of a typical impedance curve for an audio driver. The horizontal axis represents frequency in Hertz, while the vertical axis represents impedance in ohms. As shown, the impedance curve peaks at the mechanical resonance of the driver, which typically occurs at frequencies near the lower extreme of its operating range. The impedance curve then begins to rise significantly due to the inductance of the driver, which typically occurs around 1000 Hz.
Often, driver manufactures talk of a nominal impedance, but this is a kind of average. If one designs a variable impedance amplifier 300 based on nominal impedance, then it is clear that there is improper modeling of the electrical dynamics of the driver (assuming any modeling is done at all) and the results will be less than satisfactory.
Another problem with the design of the variable impedance amplifier 300 is that because the voltage and current sensing feedback paths 308 and 322 are resistive, the output impedance of the amplifier 300 remains relatively constant for all input frequencies. A considerable improvement over the variable impedance amplifier 220 would be an amplifier having an output impedance that varies as a function of frequency to achieve a number of desirable objectives.
U.S. Pat. No. 4,393,353 issued Minagawa describes an amplifier that has both a voltage and current feedback circuits in an attempt to reduce both the voltage and current distortion that would be produced by a Class A/B power amplifier stage were feedback not to be used. This scheme is predominantly a voltage feedback system except at the resonance frequency Minagawa provides current feedback in an attempt to match the impedance of the amplifier with the impedance of the driver load at the mechanical resonance peak. This is reported to have two main advantages, first to reduce current distortion and second to obtain a more even output sound response at the mechanical resonance frequency. Although in theory the output impedance of Minagawa's amplifier appears to vary as a function of frequency, and is an improvement over the variable impedance amplifier 300, the output impedance of Minagawa's amplifier only varies in a fairly narrow range of the resonance frequency of the connected driver. It appears that Minagawa attempts to reduce what is referred to as current distortion at only the resonance frequency, which also has the added effect of increasing the output of the amplifier at the resonance frequency. When describing current distortion, therefore, Minagawa appears to focus on that distortion produced by his power amplification stage, ignoring driver distortion due to nonlinearities inherent to the driver such as the nonlinearity of BEMF, and the nonlinearity of the inductance as a function of driver displacement.
Accordingly, what is needed is an improved audio amplifier that is capable of reducing driver distortion arising from the nonlinearities inherent to the driver. The present invention addresses such a need.